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Geometry Level 2

How many of the following 8 shapes must have (at least) one axis of symmetry?

equilateral triangle , right triangle , square , cyclic quadrilateral , parallelogram , rhombus , rectangle , regular pentagon \begin{array}{c}&&\text{equilateral triangle}, &\text{right triangle}, &\text{square}, &\text{cyclic quadrilateral}, \\ &\mbox{parallelogram}, &\text{rhombus}, &\text{rectangle}, &\text{regular pentagon} \end{array}


The answer is 5.

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Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

The 3 − 4 − 5 3-4-5 right triangle has no axis of symmetry. The parallelogram that is not a rhombus has no axis of symmetry. The general cyclic quadrilateral does not need to have an axis of symmetry.

The equilateral triangle, square, rectangle, rhombus and regular pentagon each must have an axis of symmetry. In fact, all of them have at least 2 axes of symmetry. Therefore, 5 of the shapes have an axis of symmetry.

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